Causal Selection of Covariates in Regression Calibration for Mismeasured Continuous Exposure

Regression calibration as developed by Rosner, Spiegelman and Willet is used to correct the bias in effect estimates due to measurement error in continuous exposures. The method involves two models: a measurement error model (MEM) relating the mismeasured exposure to the true exposure and an outcome model relating the mismeasured exposure to outcome. However, no comprehensive guidance exists for determining which covariates should be included in each model. In this paper, we investigate the selection of the minimal and most efficient covariate adjustment sets under a causal inference framework. We show that in order to correct for the measurement error, researchers must adjust for, in both MEM and outcome model, any common causes (1) of true exposure and the outcome and (2) of measurement error and the outcome. When such variable(s) are only available in the main study, researchers should still adjust for them in the outcome model to reduce bias, provided that these covariates are at most weakly associated with measurement error. We also show that adjusting for so called prognostic variables that are independent of true exposure and measurement error in outcome model, may increase efficiency, while adjusting for any covariates that are associated only with true exposure generally results in efficiency loss in realistic settings. We apply the proposed covariate selection approach to the Health Professional Follow-up Study dataset to study the effect of fiber intake on cardiovascular disease. Finally, we extend the originally proposed estimators to a non-parametric setting where effect modification by covariates is allowed.